Suppose a simple pendulum of mass m is attached to a string of length L, oscillating under the influence of gravity g. What is the form of the equation for the pendulum's time period? Initially, identify and list the variables involved in the problem. The time period T can be expressed as the product of these variables, each raised to an unknown exponent. Here, k is a dimensionless constant. Excluding the dimensionless constant, an equation relating the dimensions of the variables with the time period is obtained. Now, by equating the exponents of the dimensions on both sides and solving the equations, the values of the unknown exponents are determined. On substituting the exponents, the final expression for the time period is obtained, which is a product of the constant k and the square root of the length over gravitational acceleration. One of the limitations of dimensional analysis is that it does not allow us to find the value of the dimensionless constant k.